Pattern dependent profile distortion during plasmaetching of high aspect ratio features in SiO2

Cite as: J. Vac. Sci. Technol. A 38, 023001 (2020); doi: 10.1116/1.5132800

View Online Export Citation CrossMarkSubmitted: 19 October 2019 · Accepted: 17 December 2019 ·Published Online: 8 January 2020

Shuo Huang,1,a) Seungbo Shim,2 Sang Ki Nam,2 and Mark J. Kushner1,b)

AFFILIATIONS

1Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal Ave., Ann Arbor,

Michigan 48109-21222Samsung Electronics Co., Ltd., 129 Samsung-ro, Yeongtong-gu, Suwon-si, Gyeonggi-do 443-742, South Korea

Note: This paper is part of the Special Topic Collection Commemorating the Career of John Coburn.a)Present address: KLA Corp., 2350 Green Road, Suite 100B, Ann Arbor, MI 48105; electronic mail: shuo.huang@kla.comb)Author to whom correspondence should be addressed: mjkush@umich.edu

ABSTRACT

As aspect ratios of features in microelectronics fabrication increase to beyond 100, transferring patterns using plasma etching into underlyingmaterials becomes more challenging due to undesirable feature distortion such as twisting, tilting, and surface roughening. These distortionscan be attributed to several causes including the randomness of reactive fluxes into features, charging, and pattern dependencies. Randomnessmainly results from disparities in the fluxes of etching species into adjacent features, which can be exacerbated when reaching the etch front inhigh aspect ratio (HAR) features due to conduction limits. These stochastic variations in energy, angle, and sequence of the incident speciesinto adjacent features, rather than reactor scale nonuniformities, produce many of the feature-to-feature variations in etch performance. Patterndependent distortion results from interference between the features due to charging of the feature surfaces. The resulting electric fields act notonly on the ions incident into a given feature, but also on the ions in adjacent features. With symmetric patterns, stochastic charging of theinside surfaces of features results in tilting of HAR features in random directions. However, with nominally identical neighboring features,electrical forces on ions inside the features should, in principle, cancel. Statistical variations will produce some random tilting; but on average,there is no systematic tilting. With asymmetric patterns, horizontal electric fields are generated by feature charging that point from dense(more positively charged) to sparse (less positively charged) areas of the pattern. These net electric fields deviate ions from normal incidenceand produce systematic tilting.

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I. INTRODUCTION

In plasma etching for semiconductor fabrication, patterns aretransferred from the overlying masks to underlying features, ideallyreplicating the mask pattern.1,2 For achieving high selectivity inplasma etching, different mask materials are used such as photoresist(PR), amorphous carbon layers (ACLs), and organic planarizationlayers.3 The principle of anisotropic plasma etching is that verticallydirected ions onto the substrate will replicate the overlying patternsby activating etch processes on the horizontal bottom of the featureand not on the sidewalls. Due to the decrease in logic feature sizes,now sub-10 nm, and increase in aspect ratio (AR) for 3D NANDmemory products, feature distortion is becoming more problematic.Feature distortion is the inability to transfer the desired pattern

into the underlying material. Common distortions include twisting(a circular pattern does not produce a circular feature), tilting (thefeature is etched at an angle instead of vertically), bowing (featuresidewalls are curved instead of straight), and edge roughening (insidesurfaces of features are not smooth).

Distortions such as bowing are systematic—that is, the distor-tion appears consistently in all features. Systematic distortions suchas bowing can usually be explained by ion fluxes into the featurethat are angularly broad or having been reflected from other sur-faces. The other distortions are typically statistical—that is, theseverity of the distortion varies from feature to feature. These dis-tortions are ascribed to several causes, including charging of thefeature by ions and electrons from the plasma, polymer deposition,

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and pattern dependencies.4–6 In some cases, sidewall rougheningcan originate from distortions in the pattern in the mask, which aretransferred into the underlying materials.6,7 These mask distortionsmay originate in the lithography or during the plasma process.With increases in AR to greater than 50–100, small distortions in,for example, tilting are magnified by the depth of the feature. Theend result can be a decrease in the spacing between adjacent vias,even leading to bridging of adjacent vias.8,9

The density of a pattern of features refers to the number offeatures per unit area and is typically measured as the pitch of thepattern—the distance between the centers of adjacent features.With pitches of hundreds of nanometers to tens of nanometers,there is no systematic variation in the incident fluxes into adjacentfeatures. With mean free paths of electrons, ions, and neutrals inthe plasma greatly exceeding the pitch, there cannot be a significantgradient in reactant fluxes from the plasma incident into onefeature and its neighboring features. In these cases, the dominantsource of differences in fluxes into the adjacent features is simplythe stochastic nature of the fluxes. The features are so small thatthe fluxes (magnitude and identity of reactants) into adjacent fea-tures have a significant stochastic component. This randomnesscan be magnified in high aspect ratio (HAR) features due to con-duction limits and diffusive reflection at sidewalls for the etchingspecies.10,11 The time intervals between particles incident into thefeature are usually much larger than the transit time of the particlesin the feature, which makes the profiles sensitive to the sequence ofthe incident particles. Thus, small variations in energy, angle, andsequence of incident etching species in different features may causefeature-to-feature variations in etch performances (e.g., etch rateand selectivity).

Charging on the walls of a single feature during plasmaetching produces internal electric fields that perturb the trajectoriesof anisotropic positive ions traversing the feature. Due to the differ-ing angular distributions of electrons and positive ions, the tops offeatures typically charge negatively while the lower parts of the fea-tures charge positively. When etching nonconductive materials(e.g., SiO2 and Si3N4), the electric fields produced by charge in agiven feature can affect ion trajectories in neighboring featuresthrough the penetrating electrostatic fields.12 In addition to theintrinsic randomness of charging of small features, the electrostaticinterference from neighboring features is another source for profiledistortion and feature-to-feature variation, which now depends onthe adjacency, that is the pattern, of these neighboring features. Withthe pitch between features continuing to decrease, the electrostaticinterference from adjacent features becomes more problematic.

Etching of patterns of HAR vias by plasmas sustained influorocarbon/oxygen gas mixtures was experimentally investigatedfor via diameters of 50–200 nm and ARs of 10–30.13 Statistical vari-ations in profiles, etch rates, and pattern distortion were observedfrom feature to feature. By using a cyclic process of alternatingetching and deposition phases for SiO2 processing, bowing at lowARs (∼5) and feature-to-feature variations in critical dimensions(CDs) at high ARs (>20) were both reduced.14 The anisotropy ofthe profiles was improved due to polymer deposition on thesidewalls during the deposition phase. The polymer deposited atthe interface between the mask and the oxide significantly affectedthe degree of pattern distortion, which could be alleviated by

adding an in situ polymer removal step during the over-etch.7–15

(For brevity, the term oxide refers to silicon dioxide, SiO2, andnitride refers to silicon nitride, Si3N4.) Defects in the maskproduced by erosion during the etching process can be transferredto the sidewalls of HAR features.6 Suppressing mask degradationwas found to decrease feature distortion and alleviate twistingat high ARs when transferring patterns in ACL into SiO2 withdifferent pitch sizes.

Feature-to-feature variations become more severe when etchinghybrid materials such as alternately deposited oxide-silicon-oxide(O–Si–O) and oxide-nitride-oxide (O–N–O) stacks. In the plasmaetching of channel holes in O-Si-O stacks using HBr/fluorocarbonmixtures, the sidewall of the features changed from smooth toscalloped when the HBr fraction was increased.16 Surface adsorptionof N–H and Br was enhanced resulting in reduced polymer thicknessand enhanced Si etching. In the modeling and characterization offeature distortion during plasma etching of source/drain contacts,the consequences of random variation in the mask on distortionoutweighed systematic variations when the CD decreased below32 nm.17,18 A voxel-slab model was used to investigate contact holeetching in SiO2, showing that profile distortion due to physicaldamage in the SiO2 was reduced by maintaining a critical thicknessof the overlaying polymer.19,20 Results from a three-dimensionalMonte Carlo model indicated that ion induced surface roughnesscan be mediated by the use of etch inhibitors.21

In this paper, results are discussed from a computationalinvestigation of feature distortion during plasma etching of HARvias in SiO2 using trifrequency capacitively coupled plasmas(TF-CCPs) sustained in Ar/C4F8/O2 mixtures. The fluxes of ionsand neutrals and ion energy and angular distributions (IEADs)were obtained from reactor scale modeling performed using theHybrid Plasma Equipment Model (HPEM). The feature scale mod-eling was performed using the three-dimensional Monte CarloFeature Profile Model (MCFPM). Feature-to-feature variations inthe shape of the vias mainly result from randomness in the fluxes ofparticles into the features rather than reactor scale nonuniformities.The charging of features in symmetric patterns results in featurestilting in random directions. With asymmetric patterns, chargingproduces tilting toward open areas of the pattern due to horizontalcomponents of the E-field induced by the laterally asymmetriccharging. The tilting can be alleviated to some degree by increasingthe bias power, which increases the ion energy and decreases theetch time, resulting in less deviation in ion trajectories by theselateral electric fields.

Descriptions of the models used in this investigation are inSec. II. Results from the study for the etching of multiple vias indifferent patterns are in Sec. III. Concluding remarks are in Sec. IV.

II. DESCRIPTION OF THE MODELS

Integrated reactor and feature scale models were used to inves-tigate plasma etching of multiple HAR vias in SiO2 usingTF-CCPs. The fluxes of ions and radicals to the wafer and theIEADs were obtained from the reactor scale modeling using theHPEM (Ref. 22), which is discussed in detail in Ref. 23. AnAr/C4F8/O2 gas mixture was used. The species and gas phasereactions included in the reaction mechanism are the same as in

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Ref. 23. The resulting profile evolution and etch properties wereobtained by feature scale modeling with the MCFPM.11,24

The MCFPM is a three-dimensional voxel-based modelutilizing a cubic-mesh. Briefly, each cell in the numerical mesh mayrepresent a different solid material. Gas phase pseudoparticles arelaunched with their initial velocities sampled from the IEADsobtained from the HPEM. Pseudoparticles striking surfaces cansputter, activate chemical reactions, deposit, implant, and reflect,thereby changing the identity of the underlying mesh cell or addinga solid mesh cell. Energetic pseudoparticles can penetrate beneaththe surface to activate subsurface chemical reactions. Charged speciesstriking solid surfaces deposit charge, which produces charge densi-ties used in solving Poisson’s equation for the electric potential. Theresulting electric fields are then used to advance the trajectories ofcharged particles passing through the feature. In this investigation,the mask, SiO2, and fluorocarbon polymer deposits have essentiallyno electrical conductivity, and so the electric fields produced bycharge inside one feature can penetrate into adjacent features.

The reaction mechanism used in the MCFPM for predictingprofile evolution in SiO2 by Ar/C4F8/O2 plasmas is described inRef. 23. Briefly, the pristine SiO2 surface is activated by energeticspecies (ions and hot neutrals). The activated surface has higherreactivity for passivation by polymerizing CxFy radicals. Furtherdeposition of CxFy species on the passivated surface formspolymers, whose thickness can be controlled through etching byatomic oxygen species produced by the dissociation of the O2. Theenergetic species reaching the passivated surface (SiO2CxFy) removethe oxide in the form of volatile SiFx and COx, which is the processof chemically enhanced etching (i.e., chemical sputtering). TheSiO2 can also be directly removed from the surface throughbombardment by energetic species through physical sputtering,which requires higher threshold energies than chemical sputtering.

III. ETCHING OF MULTIPLE VIAS IN PATTERNS

The geometries and initial patterns of PR for etching multipleHAR vias are shown in Fig. 1. Two symmetric patterns of four viaswere investigated: a linear array and a 2 × 2 square pattern. Theasymmetric patterns investigated were a four via off-axis arrange-ment and linear arrays with one via missing. Gas phase particlesleaving the sides of the computational domain were reflected backinto the domain, reflective boundary conditions, while gas phaseparticles leaving the top of the domain were removed from the simu-lation. Reflective boundary conditions were also used for mesh prop-erties across the lateral boundaries of the pattern, including materialidentities and charge. With periodic boundary conditions, the unitpattern shown in Fig. 1 can represent full-pitch (for the linear arrayand square unit) and half-pitch patterns (for off-axis unit).

The distance between the centers of the adjacent vias was100 nm and the diameters of the holes in the PR mask were 50 nm.The thickness of the SiO2 was 2000 nm, with 670 nm thick PR asthe mask and Si as the stopping layer. The total aspect ratio forperfect pattern transfer from the top of a pristine mask to the stoplayer is 53. The AR of only the SiO2 is 40. Unless otherwise noted,the AR in the following discussion refers to the depth of the etchedfeature in the SiO2. The meshes consist of 40 × 160 × 1084 cells forthe linear pattern, 59 × 146 × 1084 for the off-axis pattern, and

80 × 80 × 1084 for the square pattern, producing cubic voxels of2.5 nm on a side. The dielectric constants (ϵ/ϵ0) of the materialsused in the solution of Poisson’s equation were as follows: SiO2,4.0; photoresist, 3.0; and polymer, 3.0.

The fluxes of the ions and radicals and IEADs were obtainedfrom the reactor scale modeling of a TF-CCP sustained in Ar/C4F8/O2

mixtures. The role of Ar in the mixture is primarily to provideenergetic, chemically inactive, Ar+ ions onto the surface for physicalactivation of processes. C4F8 is dissociated by electron impact toproduce polymerizing CFx and CxFy species, which deposit on thesurface of the oxide and serve as the fuel to remove silicon andoxygen sites while protecting the sidewalls. O2 is dissociated toproduce O atoms that are used to control the amount of polymerdeposition at the surface to avoid clogging while allowing etchingspecies (e.g., ions and neutral radicals) to reach deeper into features.

Three frequencies (80/10/5MHz) were used to provide a largedynamic range for tuning the plasma properties and the IEADs.The 80MHz power applied on the top electrode was mainly usedas the source power for sustaining the plasma. The 10 and 5MHzpowers applied on the bottom substrate were mainly used to accel-erate the ions to the surface with customized IEADs. For the basecase, the powers of the three frequency sources (80/10/5MHz) were400/2500/5000W. The corresponding voltages to deliver thesepowers were 125/1030/2450 V, with a dc bias of −1690 V. The ionshave high energy (1400–3000 eV) and narrow incident angles (lessthan 3°), which are desirable for HAR etching by reducing sidewallimpacts and producing anisotropic profiles.

Charging of the surfaces on the top and inside of the featureoccurs in dielectric etching or in conductor etching using polymer-izing gas mixtures. As described above, positive ion pseudoparticlesare launched toward the surface with velocities sampled from the

FIG. 1. Schematic of the patterns (linear array, off-axis, and square) in the pho-toresist and the geometries of the initial profiles. The height of the SiO2 is2000 nm with 670 nm thick photoresist as the mask and Si as the stoppinglayer.

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IEADs obtained from the HPEM. (Essentially no negative ionsreach the surface.) A corresponding flux of electron pseudoparticlesis launched toward the surface to provide a charge neutral flux. Thevelocities of the electrons are randomly chosen from an isotropicMaxwellian distribution having a temperature of 4 eV. Due to thecomputational expense of solving Poisson’s equation, the electricpotential is updated only after 400 charged particles strike thesurface. During the execution of the MCFPM, millions of chargedparticles are launched. The resulting profiles do not significantlychange when increasing the rate of solving Poisson’s equation. Thebottom of the computational domain is electrically grounded. Sincethe actual thickness of the wafer is not resolved in the MCFPM,three thin dielectric layers were added between the stopping layerand the ground plane. The dielectric constants of these layers wereadjusted so that the capacitance of the feature with respect to theground plane is the same as for the actual thickness of the wafer.

A. Statistical feature-to-feature distortion withsymmetric patterns

Sectional views during plasma etching cleaved through thecenter of the linear array as a function of time are shown in Fig. 2.The time between each frame is the same, except for the first frameshowing the profile at the very beginning of etching. When examin-ing individual vias, the general trend of profile evolution is quitesimilar to that of etching a single HAR via, as discussed in Ref. 23.Key features are captured including eroded PR mask, bowing in theupper portion of the features at AR of 5 and a tapered etch front.Due dominantly to ion sputtering, the PR is eroded during plasmaetching, resulting in a SiO2-to-PR selectivity of 10. This erosion leadsto roughness on the top, beveled surfaces, and sidewalls of the PR.

As the etching proceeds, the etch front of each via propagatesdownward (normal to the surface), without major tilting or twist-ing. As the pitch of the pattern is 100 nm, there is no systematicchange in the incident fluxes across the array. That is, there is nosystematic variation in any reactor scale plasma properties acrossthe dimension of the array. The randomness in the shape of viasand etch rates result from the stochastic nature of the fluxes ofradicals and ions incident into adjacent features. Although there isvariation in the etch rate of as much as 10% due to the stochasticarrival of reactants, by having an over-etch period, the side-by-sidefeatures do eventually bottom-out on the stopping layer in a fairlyuniform manner.

With the diameter of the hole in PR being 50 nm and fluxesincident into the hole being about 1015 cm−2 s−1 for ions and1017 cm−2 s−1 for neutral radicals, the ions and radicals arrive intothe feature with time intervals of 10−5 and 10−7 s, respectively. Forion and hot neutral energies in excess of 1000 eV and the thermalneutrals of 0.03 eV, the transit time through the feature or theresidence time within the feature before leaving is about 10−10 s(for ions and hot neutrals) and 10−8 s (for thermal neutrals).Having said that, there may be tens to hundreds of reflections ofthermal neutral particles within the feature before exiting. Thesereflections could extend the residence time to as long as 10−6 s.Even for these long times, the likelihood of having multipleparticles in the feature (or having particles interact in the feature)is small.

The statistical variation in fluxes results in adjacent featuresreceiving different mole fractions of species having differentsequences of arrival, and different energies and angles of each indi-vidual species. These differences produce feature-to-feature variations

FIG. 2. Section view (top) and central slice (bottom) of profile evolution duringetching of HAR features in a pattern of four linear vias. The first frame is at thebeginning of the etching, while the other four frames are sampled with the sametime interval.

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in etch properties. These differences generally cannot be rectified oraveraged out without increasing the number of particles arriving inthe feature by increasing the magnitude of fluxes. Due to the finiteangular spread of ions, nonspecular reflection of energetic particles,and gas conduction limits, the fluxes of energetic particles (ions andhot neutrals) and radicals decrease by factors of 10 and 50, respec-tively, as the AR of the via increases from 0 to 40. This decrease influxes increases the randomness and stochastic variation in theetching species reaching the etch front. The MCFPM uses pseudopar-ticles that individually represent hundreds of atoms. This weightingexaggerates these stochastic effects in sampling the pseudoparticlesfrom the total fluxes as well as sampling the energy and angle of theions from the IEADs.

As the AR increases during etching, the feature-to-feature var-iation becomes reinforced, rather than being attenuated, due tothere being fewer ions and radicals reaching deeper into featuresthat are then more subject to randomness. Although there is nosystematic tilting, individually features do tilt in random directions.The tilting has many origins. A statistically thicker layer of polymeron one side of the feature will produce a different angular distribu-tion of specularly or diffusively reflected ions, which may preferen-tially etch the opposite wall. (Here, the term ion refers to both theincident charged particle and the hot neutral produced when theion first strikes a sidewall.) Statically, more positive charge on oneside of the feature, which may be trapped in polymer, will perturbion trajectories toward the opposite side of the feature. Once tiltingdevelops at low ARs, the tilting will be enhanced and transferreddeeper into the feature, rather than being rectified or reversedunless the physical origin of the asymmetric trajectories in thefeature is changed. That is, if positive charge is asymmetricallytrapped in polymer on the sidewall, all subsequent ion trajectorieswill be perturbed until that trapped charge is removed or neutral-ized. Taking the linear array pattern as an example, the secondfeature from the right slightly tilts rightward while the first featurefrom the right slightly tilts leftward starting from an AR of 20, asshown in Fig. 2. As the AR increases to 40, the tilting directions ofthese two features are maintained. The end result is that their etchfronts approach each other to a distance of 90 nm, which is smallerthan the pitch in the PR pattern by 10 nm (10% loss in pitch).

The charge densities deposited at the top and inner surfaces ofthe features, and the electrostatic potentials produced by thesecharges, are shown in Fig. 3 for the same time intervals as in Fig. 2.The electrons predominantly deposit charge on the top surfaces,beveled surfaces, and the shallow sidewalls of the PR, reaching amaximum of −46.4 C/cm3 on the beveled surface of the PR.Positive ions reach more deeply into features due to their aniso-tropic IEADs. The positive ions deposit their charge on the surfaceand reflect as hot neutrals. For small AR, the ions initially strikethe bottom of the feature, and this is the location of the maximumin positive electric potential. With increasing AR, ions (having afinite angular spread) will eventually strike the sidewall and depositcharge on the sidewall. Beginning with an AR of about 15, the elec-tric potential has its maximum potential on the sidewalls at thisdepth. An electric field is established pointing from the middle ofthe feature upward toward the top of the feature, and downwardinto the feature. A near quasisteady state is established wherein therate of charging of the feature by positive ions is balanced by

FIG. 3. Time evolution of charge distribution (top, section view) and electricpotential (bottom, central slice) during etching of HAR features in a pattern offour linear vias. With reflecting boundary conditions, the pattern is symmetric.The frames are sampled at the same time as in Fig. 2.

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electrons attracted into the feature by the upward pointing electricfield.

Ions incident into the feature with a small angle and energygreater than the maximum in electrostatic potential will decelerateand then accelerate when approaching and passing the maximumin potential. The ions will reach deeper into the feature with adecrease in their energy determined only by the local electricpotential and not the maximum in electric potential. This is a fun-damentally different situation than when the maximum in electricpotential is on the bottom of the features. Ions that neutralize bystriking the sidewall above the maximum in electrostatic potentialproduce hot neutrals that proceed deeper into the feature unaf-fected by the electric fields. In large part, ions whose trajectoriesare perturbed by these in-feature electric fields to produce tiltingare those ions that either pass by or neutralize near the maximumin electric potential.

Due to the stochastic variations in the number, sequence,energy, and angle of the incident particles into the features, theprofiles in Fig. 2 have a maximum of 7% difference in etch rate and5% difference in the bowing CDs. One solution for mitigating thefeature-to-feature variation in the etch rate and CD at the bottomof the feature is to allow for some significant over-etch time toensure that all the features are etched through and the bottom CDsare wide enough for the subsequent process step. The surfaces ofthe final etch profiles with 10% over-etch are shown in Fig. 4 fordifferent patterns. By allowing for 10% over-etch, the etch fronts allreach the stopping layer with at least a 20 nm hole opening at thebottom. The bowing CDs vary from feature to feature by less than5%, with the maximum bowing CD being 72 nm. Overall, the stat-istical disparities in feature profiles can be diminished by allowingfor over-etch, which increases the total fluence of particles into thefeature.

In radio frequency (RF) excited plasmas, ions are acceleratedtoward the surface by the electric field in the sheath resulting in anearly continuous flux onto the surface. Electrons reach the surfacedominantly during the anodic portion of the RF cycle. After initialnegative charging of the surface to produce the floating potential,equal fluxes of electrons and ions averaged over the RF cycle resultin a charge neutral flux to flat surfaces. Patterned surfaces withHAR features enhance or restrict the relative fluxes of electrons andions to surface inside the features due to the difference in theangular distributions of the electrons and ions. The end result is aspatial variation of the charge distribution and thus electric poten-tial along the inner sidewalls of the features in SiO2. A linear arraywith reflective boundary conditions is equivalent to having an iden-tical mirror image of the array across the boundary or features witha constant pitch in every direction. With the resulting symmetriccharge distribution, the electric potential at a given height is quiteuniform, as shown in Fig. 3. Any feature-to-feature variation inelectric potential is due to statistic variation in charging and is sys-tematic. The symmetric charge distribution produces electric fieldsthat act on adjacent features from both sides, producing no netelectric fields that would systematically deflect ion trajectories.There may be some random interference between features, but nosystematic interference.

Ideally, the initially circular mask opening in the PR should befaithfully transferred to the feature during plasma processing. Due

to nonuniformities in mask materials and stochastic processesduring plasma etching, feature distortion such as contact edgeroughness (CER), line edge roughness, or elliptical profiles candevelop.7,25,26 Profiles through square and linear symmetric pat-terns after a 10% over-etch are shown in Fig. 4. These profiles areshown with the polymer removed indicating the shape of theprofiles that would result after a perfect cleaning process. Theinitial mask opening is shown by the dotted circles. Profile outlineswider than the opening indicate bowing, which is most severe atAR = 5–10. Profile outlines narrower than the mask openingindicate tapering. Profile outlines that are noncircular indicatedistortion. If the centroid of the profile is not at the center of thecircle, then the feature has tilted.

The horizontal sections shown in Fig. 4 are close to circular,though with some bowing, for ARs < 20. For larger AR, the profilesbegin to distort. With AR > 30, the profiles have smaller diameters(<50 nm) and more anomalies due to tapering of the etch front.The distortion is due to the stochastic nature of the reactants enter-ing the feature and is worse deeper in the feature that receives lessflux due to conduction limits and hot neutrals having less energythan the original ions. Locations deeper in the feature also

FIG. 4. Horizontal slices through multiple vias showing the edge of the SiO2

surface for aspect ratios of 10, 20, 30, and 40 after a 10% over-etch. (a) Linerarray, (b) off-axis, and (c) square patterns. The dotted circles are projections ofthe initial hole in the PR mask.

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experience less local over-etch that tends to round-out the feature.Distortion is in large degree statistical. With symmetric patterns,there is some random tilting due to random surface charging inboth the feature and adjacent features. However, this tilting is notsystematic—that is, there is not an array wide trend in tilting.

As the etching proceeds, the PR is eroded dominantly by ionsputtering, resulting in the PR having rough beveled and top sur-faces as shown in Fig. 2. The features at the PR level become lessdistinct as the beveled surfaces of adjacent holes intersect those oftheir neighbors. If the PR erodes to the extent that the beveled sur-faces reach the SiO2 interface, scattering of the ions from theroughened beveled surfaces into the feature will enhance bowing, asituation that does not occur here due to the large initial height ofthe PR. The roughening of the PR will produce some channeling ofgrazing ions scattering from the inner surface of the PR that can bea source of CER in the SiO2. For these conditions, little CER wasobserved from this source. The major effect of the roughness of thePR was diffusive scattering of grazing ions, which contributes to theedge roughening and bowing by having more normal incident ions.

The CER mainly originates from the randomness in theenergetic ions and polymerizing radicals into the features. Due tothe small number of ions into the feature, the activation energyprovided by the ions will not be uniformly distributed along thecircumference of the feature at all ARs during the whole processingtime. Nonuniform polymer deposition on the sidewalls adds to theroughness produced by ions by providing sites for diffusive scatter-ing and nonuniform passivation of SiO2. This effect is exacerbatedat high AR (>30) where surface coverage by polymer is spotty dueto conduction limits for transport of polymerizing radicals deepinto the feature and redeposition of etch products. The distortiontends to be self-perpetuating as once the feature becomes noncircu-lar, specular ion scattering from the sidewalls is channeled to lowerin the feature to replicate the same topology. This is again exacer-bated at high AR where polymer coverage is less due to conductionlimits. With sufficient polymer flux, dents and grooves in the side-walls tend to be filled in by the polymer.

The deposition of polymer on the sidewalls for AR < 10 has athickness of about 10 nm. This is in part due to the slowing of ionsby the positive charging deeper in the feature, which reduces therates of polymer sputtering and provides additional polymerizingradicals due to neutralization of slower CFx

+ and CxFy+ ions. The

thicker polymer effectively increases the AR of the feature from40 to closer to 50 by narrowing the open area. The larger effectiveAR then reduces fluxes deeper into the feature by worsening theconduction limited transport. The sidewall passivation is itselfsomewhat stochastic. All of these effects work against transport ofneutral radicals deeper into the feature and work against specularreflection of ions from the sidewalls. The edge profiles at AR = 40are then anomalous with small openings (less than 30 nm) evenafter 10% over-etch.

The horizontal slices at an AR of 40 are shown in Fig. 5 forthe linear array after 10% over-etch with and without charging.(The effects of charging can be partly mitigated by fluxes of highenergy electrons into the feature4 or the use of pulsed power.27)The edge profiles shown in Fig. 5(a) for the noncharging case havelarger hole openings (∼50 nm), similar to the initial hole openingin PR. As the etch rate without charging is about 20% higher than

with charging due to ions not being decelerated by the electricpotential in the feature, a 10% over-etch results in more opening ofthe SiO2 after reaching the Si stopping layer.

The profiles shown in Fig. 5(b) with charging are for differentvalues of the random number generator seed in the simulation. Asequence of pseudorandom numbers is used to choose fluxes, scat-tering angles, and surface reactions during the simulations. Using adifferent random seed has the effect of sampling different parts ofthe die with statistically different incident fluxes while having thesame time averaged values. The centroids of the profiles at AR = 40for 10 cases with different random number seeds are shown inFig. 5(c). The profiles with charging are more distorted andmore-stochastic than in the absence of charging. The centroid ofthe feature for any given case will likely land somewhere other than

FIG. 5. Horizontal slices at the bottom of the SiO2 (AR = 40) for final etch pro-files with 10% over-etch for a symmetric linear array pattern. (a) Without charg-ing, (b) with charging for different random number seeds in the simulation, and(c) statistics of the centers (denoted by “+”) of the profiles at AR = 40 for 10cases with charging. The dotted circles are projections of the initial hole in thePR mask.

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directly under the center of the hole in the PR. That is, individualfeatures do have random tilting, deflecting the center of the bottomof the feature by 10–20 nm. However, when averaged over manyfeatures, centroids of the individual features cluster around thecenter of the hole. That is, there is no systematic distortion ortilting of the features.

B. Feature properties with asymmetric patterns

Asymmetric pattern of features occurs at the edge of a die orwhen features with different sizes and shapes (e.g., circular,L-shape, and U-shape) are adjacent and simultaneously etched.13

Imperfections in the lithography process can produce nonuniformpatterning, which leads to local asymmetries within a large matrixof vias.19,28 In this investigation, we investigate deliberately asym-metric patterns by removing one feature in the linear array.

The final etch profiles with 10% over-etch and horizontalslices at different ARs for the asymmetric linear pattern are shownin Fig. 6(a). The final profiles for AR = 40 for several cases with dif-ferent random number seeds and the location of their centroids areshown in Fig. 7 as the 5 kW case. The fluxes and IEADs used hereare the same as the base case with the symmetric pattern. Insteadof random tilting of the features as with the symmetric patterns inFig. 4, the features in the asymmetric pattern preferentially tilt inthe direction of the missing via or toward open areas or less denseportions of the pattern. The tilting angles of the features adjacentto the missing via are larger than the more distant features. Thecollection of centroids of 10 cases [Fig. 7(b)] indicate that tiltingfor the asymmetric pattern has a systematic distortion.

The systematic tilting with the missing via results from thepattern level asymmetry in the charge distribution. As shown inFig. 3, a positive electric potential is produced inside features. Anelectric field points radially outward from positive charged. Althoughthere is statistical variation in the charging in each feature, on theaverage, the maximum electric potential occurs at about the sameheight. As a result, the electric field in a symmetric pattern from onefeature is balanced by an oppositely pointing electric field from anadjacent feature. The end result is little lateral deflection of ions.

With an asymmetric pattern, the electric fields pointing awayfrom the feature at the edge of a pattern is not balanced by anopposing electric field. This leaves a net electric field pointing fromthe dense to the less dense portions of the pattern. The direction ofthe electric field generally points up or down from the maximumin electric potential, as shown in Fig. 6(b). The upward pointingvertical component of the electric field is responsible for slowingions approaching the maximum in potential. The downward point-ing vertical component of the electric field is responsible for accel-erating ions that are able to pass by the maximum in potential.Meanwhile, in the lateral (horizontal) direction, there is a net elec-tric field component pointing toward the less dense pattern. Theskewing of the electric field toward the less dense pattern is mostsevere at an AR of 11 where the horizontal electric field reaches amaximum of 4.5 × 105 V/cm. The trajectories of the incident ionsare deviated by this horizontal electric field, resulting in tilting ofthe features in the same direction. An extreme case of producingelectric fields pointing from dense to less dense patterns would bevias at the edge of the die bordering open field. Due to the smaller

total amount of charge deposited in the asymmetric array, themaximum electric potential is 810 V, smaller by 22% than that forthe symmetric array.

The asymmetric pattern with a missing via also produces non-uniform PR isolation between the vias. The right two vias in Fig. 6

FIG. 6. Horizontal slices through an asymmetric pattern (1 via removed fromthe linear array) with 10% over-etch for ARs of 11, 20, 30, and 40. (a) Fullfeature and profile showing the outline of the SiO2. (b) Electric potential for allfeatures (central slice) and electric field vectors in the horizontal plane. Themaximum electric potential occurs at AR = 11 where the direction of the totalelectric field is shown. The electric field vectors for each AR are separately nor-malized with the maximum electric field noted in the figure.

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are isolated by PR having 50 nm thickness while the left two viasare isolated by PR having 150 nm thickness. This difference resultsin more height loss for the thinner PR than the thicker PR byabout 80 nm. In this study, the PR retains a height of more than400 nm at the end of the process. As a result, the difference in PRheight loss due to the pattern asymmetry has little effect on thefeature profiles in the oxide. However, for shorter PR mask heightsthat allow reflections from the PR bevels into the feature, the differ-ential PR height loss may be a source of difference in etch proper-ties and profiles for adjacent vias in a pattern.

The horizontal profiles at an AR of 40 for asymmetric patternswith different random number seeds are shown in Fig. 7(a) for a

5 MHz power of 5 kW. The centroids of ten profiles with differentrandom number seeds for 5MHz powers from 5 kW to 10 kW areshown in Fig. 7(b). In addition to statistical variation caused by therandomness of fluxes, the features have systematic distortion inthe form of tilting from dense to less dense parts of the pattern. Inthis case, the tilting is toward the open space of the missing via. Thetilting distortion is most severe for the vias adjacent to the open area,while less severe for the vias more distant from the open area. Thehorizontal profiles for the off-axis array shown in Fig. 4(b) showssome evidence of tilting toward the open area, though the effect isless weak as there is “open area” on multiple sides of vias.

With an increase in 5MHz power from 5 kW to 10 kW, theaverage ion energy increases from 1900 to 2500 eV and the flux ofions increases from 0.9 × 1016 to 1.2 × 1016 cm−2 s−1. The combina-tion of higher energy ions having larger fluxes results in an increasein the etch rate by about 55%, which also reduces the time requiredfor a 10% over-etch. The lower fluence of charged particles that thefeatures are exposed to results in the maximum positive electricalpotential in the feature decreasing from 810 V (5 kW) to 750 V(10 kW), about a 7% decrease, while ion energies, on the average,are higher (by about 30%). There is qualitatively a decrease insystematic tilting with higher bias over this range of powers,though the distortion is not eliminated.

C. Sparse and dense patterns

The pitch between features is generally decreasing in concertwith the decrease in feature size.28,29 For example, the HAR fea-tures in 3D NAND memory have less than 100 nm pitch. Thedistortion of features is generally more severe for smaller pitch.6

The arrangement of features may be nonrectilinear (e.g., honey-comb patterns) to increase feature density while also optimizingisolation.7,30 To investigate the dependence of feature distortionon pitch, HAR etching of symmetric patterns was simulatedfor layouts ranging from dense (pitch 80 nm) to sparse (pitch of200 nm). These patterns were created by applying reflective boun-dary conditions on all boundaries of a cell having the pitch width.The diameter of the hole in PR is 50 nm for all patterns. Followinga 10% over-etch, the centroids of the profile at the bottom of thefeature (AR = 40) at the Si stop layer were recorded for 10–20 caseshaving different random number seeds. The locations of centroidsare shown for 100, 150, and 200 nm pitches as in Fig. 8(a). Theaverage displacements of the centroids and standard deviations areshown in Fig. 8(b).

The net positive charge accumulating in any single feature forthe same incident fluxes is generally the same. However, the closerproximity of features for dense patterns results in the electricalpotential being larger than in the sparse patterns. For example, themaximum in feature electrical potential for the 100 nm pitch was≈1000 V while that for the 200 nm pitch was ≈300 V. The resultingdecrease in energy for ions penetrating deeply into features withthe dense 100 nm pattern decreases the etch rate by 40% comparedto the sparse 200 nm pattern. With the closer proximity of the stat-istical charging in neighboring features with the dense pattern, theperturbing electric fields from neighboring features are larger. Theresulting perturbation in ion trajectories then produces more statis-tical variation in the location that the feature lands on the stopping

FIG. 7. Horizontal slices at the bottom of the SiO2 (AR = 40) for final profileswith 10% over-etch for the asymmetric linear pattern (1 via removed). (a) Withcharging while changing the random number seed in the simulation. (b)Statistics of the centers (denoted by “+”) of the profiles at AR = 40 for 10 caseswith charging for different 5 MHz powers. The dotted circles are projections ofthe initial hole in the PR mask.

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later. The centroids of features with patterns below 100 nm vary byas much as 10 nm compared to only a few nanometers for thesparsest patterns. Given that the patterns are symmetric, there is nosystematic tilting of the features. The trend of more statistical dis-tortion and random tilting with dense patterns agrees withexperiments.6

D. Mobility of charges in the polymer

All of the materials in this simulation (e.g., photoresist, SiO2,and polymer) are nominally dielectrics. As a result, we assumedthat there was a negligible mobility for charges for transport onand through these materials in the simulation. In measurements byShimmura et al.,5,31 evidence was found for fluorocarbon polymerhaving some conductivity during plasma conditions similar tothose in HAR contact etching. In their experiments, polymer wasdeposited in a SiO2 contact hole having a p-Si (polysilicon)bottom. Measurements of contact potentials indicated charge dissi-pation through the polymer to the conductive p-Si below. Themobility of charges in bulk PTFE (polytetrafluoroethylene, a firstorder model for the fluorocarbon polymer in features) has valuesof 10−11−10−9 cm2/V s, which would produce negligible dissipationof charge.32,33 The experimentally observed conductivities of thepolymer then resulted from, for example, energetic particle bom-bardment (e.g., ions and VUV photons) or nonbulk properties ofthe film.

In our simulations, there are no conducting materials incontact with the polymer, as in the experiments by Shimmuraet al.5,31 As a result, any mobility of charges in the polymer wouldnot conduct away charge out of the feature. There could, however,be redistribution of charge within the feature. To investigate thispossibility, we performed computational experiments of etching oftwo-dimensional (2D) trenches using the same plasma conditionsas for the base case. Mobilities were specified for charge motion onand through the polymer. The values of mobilities investigatedwere from zero to as high as 50 cm2/V s for both positive and nega-tive charges. A mobility of 50 cm2/V s is more than 109 times largerthan found in bulk PTFE. The results of the simulation showed anegligible effect of charge mobility in the polymer on the distribu-tion of charges and electric potentials unless the mobility hasvalues of as large as 1–10 cm2/V s. For example, the electric poten-tial and charge distribution in the 2D feature are shown in Fig. 9 forhaving no mobility of charges in the polymer and having mobilitiesof 50 cm2/V s for both positive and negative charges. Due to redistri-bution of the charge in the polymer and some recombinationbetween positive and negative charges in the polymer, there is areduction in the maximum electric potential from 585 to 501 V withmobilities of 50 cm2/V s. However, these values of mobility are manyorders of magnitude larger than those for bulk PTFE. There were nosignificant changes in the etch profile.

Given the large value of mobilities in the polymer required toproduce significant changes in charge distribution and potential,the consequences of there being mildly conductive polymer for oursimulation conditions are likely not to be large. However, the issueof conductivity of polymer in HAR etching is extremely relevant,particularly for feature architectures that have conducting materialswhere charge dissipation away from the feature through those

FIG. 8. Statistics of the centroids of the profiles at AR = 40 for 10–20 caseswhile varying the pitch of symmetric patterns. (a) Location of the centroids(denoted by “+”) for pitches of 100, 150, and 200 nm. The dotted circles areprojections of the initial hole in the PR mask. (b) Average displacement(with standard deviation error bars) of the centroids of the profiles from thecenter of the mask as a function of pitch.

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conductive materials can occur. The observations by Shimmuraet al.31 that polymer conductivity depends on the structure of thepolymer is particularly relevant, as the structure is a sensitive func-tion of the fluorocarbon gas mixtures used.

IV. CONCLUDING REMARKS

The etching of multiple HAR vias in different patterns (array,off-axis, and square) by TF-CCPs sustained in Ar/C4F8/O2 mix-tures was investigated using integrated reactor and feature scalemodeling. In general, the feature-to-feature variations in etch ratesand profiles mainly result from the randomness of the fluxes intoadjacent features when the CDs decrease to a few tens of nanome-ters. The randomness is enhanced in deeper features due to theconduction limit of the incident natural radicals and roughening ofsidewalls, both of which produce more statistical and smaller fluxesdeep into HAR features. By allowing for some significant over-etch,the severity of randomness on feature distortion can be mitigatedbut at the cost of introducing systematic distortion such as addi-tional bowing.

One cause of pattern dependent distortion in dielectricetching is perturbation of ion trajectories by the electric fields pro-duced by charging in adjacent features. This perturbation of iontrajectories produces tilting. For features having symmetric pat-terns, the tilting tends to be random but not systematic. That is, theaverage location of the centroids of features at the stopping layer(here, at AR = 40) is generally directly under the opening in the PR.With symmetric patterns, the electric fields in a given feature pro-duced by charging in adjacent features are, on the average, balancedby the electric fields produced by adjacent features on the oppositeside.

With asymmetric patterns, the electric field due to charging inadjacent features is skewed to point from more dense to less denseareas of the pattern. That is, there is a net electric field that pointsfrom the dense regions of the pattern that are charged, on theaverage, more positively per unit area toward less dense regions ofthe pattern that are charged, on the average, less positively. The tra-jectories of ions are then deviated by the net horizontal electricfield pointing toward the less dense pattern, producing (on theaverage) a systematic tilt in features toward the less dense pattern.The closer the proximity of a feature to the less dense pattern (e.g.,adjacent to a vacancy in the pattern or at the edge of a pattern), theworse the systematic tilt. By increasing bias power, the energy ofions into the feature increases while the etch time decreases, result-ing in some mitigation of the systematic tilting.

Simply because a region of the pattern is positively chargeddoes not immediately imply an outward pointing tilt. It is the direc-tion of the electric field in the features that is the important param-eter. For example, if a region of the pattern is charged lesspositively than another region, the electric field will point towardthe less positively charged region, which locally appears negativelycharged, producing an inward pointing tilt. Although in featurecharging is typically positive, the tops of features can be negativelycharged, producing tilting or broadening of shallow features forions having moderate energies. The more energetic the electronsthat charge the top of the features, the larger the negative potentialwill be, extending the range of ion energies that are affected.

ACKNOWLEDGMENTS

This work was supported by the Samsung Electronics Co. Ltd.This material is also based upon work supported by the U.S.Department of Energy (DOE), Office of Science, Office of Fusion

FIG. 9. Consequences of charge mobility, μ, through the polymer on electricpotential and charge distributions for etching of a 2D trench in SiO2 for the basecase conditions. Potential and charge density for (left) μ = 0 and (right)μ = 50 cm2/V s. The electric potential is plotted with color contours. The chargedensity along the inside of the feature is color coded blue for negative and red forpositive. The ranges of potential and charge density are noted by each image.

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Energy Sciences General Plasma Science Program under AwardNos. DE-SC0001319, DE-SC0014132, and DE-SC0020232. Theauthor M.J.K. thanks Richard van Haren for discussions on sourcesof distortion.

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